C m 3 
of the Pendulum, we might have other Equations, 
which with the foregoing Equation A, would deter- 
mine the Coefficients & Exponents now mention’d ; 
but we (hall foon fee the Impoffibility of this upon two 
Accounts : Firft, There need be only two Obferva- 
tions, as to what concerns the Length of the Pendulum. 
For becaufe by Art. XVII. the Augmentation of the 
Gravity from the Equator to the Pole is proportional 
to the Square of the Sine of the Latitude, two Obfer- 
vations as much determine the Problem as an infinite 
Number can do : So that we could have but one other 
Equation befides the foregoing. This Equation will 
The firft Member of this Equation expreffes the Gra- 
vity at the Equator fubtraded from the Gravity at the 
Pole, and divided by the Gravity at the Equator ; a 
Quantity which may be known in Numbers, by deter- 
mining the Length of the Pendulum at two different 
Latitudes. The other Member of the Equation is an 
Expreffion of the fame Quantity, as it is deduced by 
the preceding Calculus. 
Secondly, This new Equation B cannot be of any 
Service in determining the Coefficients and Expo- 
nents f, g, p, q, <&c. For we fhail now (hew, that the 
foregoing Ratio P~P has fuch an immediate Con- 
P 
nexion with «, that one of them being determin’d* 
the other wiU neceffarily be fo too, independently of 
/ 
H-p x s+p ^+qxs+g 
be (B) £23? 
P 
P p 
